Is there any perfect cube that becomes a perfect square if you add 7 to it?

Checking up to 10,000,000 cubed + 7 still finds no perfect squares:

 5   point 9
10   for I=1 to 10000000
20     C=I*I*I
30     Sr=int(sqrt(C+7)+0.5)
40     if Sr*Sr=C+7 then print I,C,Sr,C+7
50   next

suggesting that a proof of impossibility is in order.

Posted by Charlie on 2007-08-03 09:37:38